{"id":"W1626279717","doi":"10.1007/3-540-07171-7_15","title":"Hadamard's generalization of hyperbolicity, with applications to the hopf bifurcation problem","year":2008,"lang":"en","type":"book-chapter","venue":"Lecture notes in physics","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia","funders":"","keywords":"Hadamard transform; Generalization; Hopf bifurcation; Mathematics; Pure mathematics; Bifurcation; Mathematical analysis; Physics; Nonlinear system; Quantum mechanics","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0001136946,0.000302638,0.0004617145,0.0000772921,0.00007612292,0.0000220509,0.0002901171,0.0002347353,0.00002582119],"category_scores_gemma":[0.00006023522,0.0002008218,0.00009795581,0.0001810275,0.00008835304,0.00003580294,0.00007485703,0.0003282952,0.00001719749],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000640001,"about_ca_system_score_gemma":0.00006921701,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001849817,"about_ca_topic_score_gemma":0.0001576937,"domain_scores_codex":[0.9987068,0.00001947906,0.0004286241,0.0002883519,0.0003852777,0.0001714481],"domain_scores_gemma":[0.9983218,0.0003993849,0.0003666115,0.0006588884,0.0002084271,0.00004483943],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00001157106,0.0001185294,0.00001629369,0.000378391,0.00006716654,9.477544e-7,0.0008850707,0.006505243,0.0001028136,0.9671867,0.0003840608,0.02434316],"study_design_scores_gemma":[0.0001355495,0.00005896267,0.00001029791,0.0002733448,0.00008933349,0.000006589304,0.000001367671,0.003594001,0.0004271108,0.9776344,0.01747798,0.0002910679],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.0001451545,0.00009310158,0.9395468,0.00071528,0.00002416117,0.001725562,0.00006535733,0.00004186798,0.05764269],"genre_scores_gemma":[0.3899906,0.001253286,0.572679,0.002967078,0.003924357,0.001928617,0.001093613,0.001029684,0.02513379],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.3898454,"threshold_uncertainty_score":0.8189273,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02738908623132601,"score_gpt":0.267631927232004,"score_spread":0.2402428410006779,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}